where \(\widetilde{T}\)  is a diagonal surrogate for \(T\) . The inverse \(\widetilde{S}^{-1}\)  can be applied inexactly by means of an AMG operator, which can be efficiently used in mechanical problems preserving a linear complexity with respect to the problem size. This is a key property to guarantee the solver scalability. Recent examples of effective AMG preconditioners are, for instance, taken from the References [1]}, [2]}, [3]}, [4]}. In this work, we use an aggregation-based multigrid as
the reference AMG operator. Specifically, the application of \(\widetilde{S}^{-1}\)  is approximated by GAMG [5]}, the
state-of-the-art aggregation based multigrid provided by the PETSc package
[6]}.
